Fault Tree

What is Fault Tree Analysis? 

Fault Tree Analysis (FTA) is qualitative top-down failure analysis method using decision tree structure to model course of accidents and analyze it. It is used in many high risk industries including aerospace, nuclear power and chemical industries.

Particular factors that could lead to an accident and their potential consequences are shown by Fault Tree which describes dependencies between potential main accident and its causes. Identified causes are associated and can be described (among others) as specific device or machine failures, human errors or environmental conditions. Fault Tree is therefore a graphical model of causal relationship - Fault Tree schema illustrates causes whose effects are defined as unsure events or risks.

The undesired outcome is taken as the root (or top event) of Fault Tree. Working backwards immediate event's causes and logical relationships between them are determined using logic gates. By stepping back through events the most basic causes are identified and Fault Tree is constructed.

Fault Tree Analysis helps to:

• understand logic leading to main failure
• prioritize events leading to top event by their contribution
• better manage resources

Probabilitiy of each fault is specified by membership function. Logical operators between faults produce membership functions of faults higher in hierarchy. Currently there are two logic gates available in Safety Analysis project - AND and OR gates.

The result of logic gate OR operation on faults is given by formula:

for independent faults:

In fault trees probability  is usually small and error resulting from omitting this part leads to overstating of real probability of top event which is appropriate direction. Therefore independence of faults is presumed and the following formula is in use:

Membership function for fuzzy sets will be calculated as:

 for trapezoidal-shaped membership function

 for triangular-shaped membership function

If  then value of 1 will be used.

The result of logic gate AND operation on faults is given by formula (independence of events presumed):

Resulting membership function will be non-trapezoidal membership function.
In Safety Analysis project resulting membership function will be approximated as:

 for trapezoidal-shaped membership function

 for triangular-shaped membership function

This approximation overstate real probability of fault which is appropriate direction.

Fault Tree XML Format

FaultTree Fields

   root - event tree identity

   faultMap - map of failures, contains at least one entry section

   scale - (LINEAR or LOGARITHMIC)

Root fields

   name

   triangleFunction→name - function name

<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<faultTree>
    <root>
        <name>root</name>
        <triangleFunction>
            <name></name>
        </triangleFunction>
    </root>
    <faultMap>
           <entry>
             ...
           </entry>
           <entry>
             ...
           </entry>
    </faultMap>
	<scale/>
</faultTree>

Entry

Entry and Entry → Value fields

   key - entry key

   value - entry value

   value→name - value name

   value→triangleFunction→name - function name

Parent fields

   name

   logicGateType - GATE_AND or GATE_OR

   triangleFunction→name - function name

<entry>
    <key>fault2</key>
    <value>
        <name>fault2</name>
        <parent>
            <logicGateType>GATE_AND</logicGateType>
            <parent>
                <name>fault1</name>
                <parent>
                    logicGateType>GATE_OR</logicGateType>
                    <parent>
                        <name>root</name>
                        <triangleFunction>
                            <name></name>
                        </triangleFunction>
                    </parent>
                </parent>
                <triangleFunction>
                    <name></name>
                </triangleFunction>
            </parent>
        </parent>
        <triangleFunction>
            <name>dużo3</name>
        </triangleFunction>
    </value>
</entry>